‎Mathématiques‎

‎"FREDHOLM, IVAR.‎

‎Sur les équations de l'équilibre d'un corps solide élastique. - [FREDHOLM'S DOCTORAL DISSERTATION]‎

‎Berlin, Stockholm, Paris, Almqvist & Wiksell, 1900. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 23, 1900. Entire volume offered. Stamps to title page and wear to extremities, otherwise a fine and clean copy. Pp. 1-42.[Entire volume: (4), 416 pp].‎

‎"FREDHOLM, IVAR.‎

‎Sur une classe d'equations fonctionnelles. - [ANTICIPATION OF HILBERT SPACES]‎

‎Stockholm, Beijer, 1903. 4to. As extracted from ""Acta Mathematica, 27. Band]. No backstrip. Fine and clean. Pp. 365-390.‎

‎"FUSS, NICOLAUS (NIKOLAI IVANOVICH FUS). - A PRIZE WINNING MEMOIR ON COMETS.‎

‎Recherches sur le Dérangement d'une Comète qui passe prés d'une Planete.‎

‎(Paris, Moutard, 1785). 4to. Extracted from ""Mémoires fe Mathematique et de Physique, Présentés à l'Academie des Sciences par divers Savans"", Tome X. Pp. 1-64 (having its own titlepage). 1 folded engraved plate. Wide-margined, clean and fine.‎

‎First printing of the prize winning memoir on the perturbations of a comet.""Fuss was an honorary member of the Berlin, Swedish, and Danish academies. In 1778 the Paris Academy of Sciences awarded him a prize for his astronomical paper ""Recherche sur le dérangement d’une cométe qui passe prés d’une planète"" ....Fuss was born into a Swiss family of modest means. His mathematical abilities, which manifested themselves quite early, attracted the attention of a number of prominent scholars, including Daniel Bernoulli, who in 1772 recommended him to Euler, then living in Russia, as a secretary. Fuss arrived in St. Petersburg at the age of seventeen and spent the rest of his life in Russia.""(DSB).‎

Referenz des Buchhändlers : 44926

‎"GAUSS, CARL FRIEDRICH.‎

‎Demonstratio Nova Theorematis Omnem Functionem Algebraicam Rationalem Integram unius Variabilis in Factores Reales Primi vel Secundi Gradus resolvi posse (i.e. English: ""A new proof of the theorem that every integral rational algebraic function of one... - [GAUSS'S DOCTORAL THESIS - HIS FIRST GREAT WORK]‎

‎Helmstadt, C. G. Fleckeisen, 1799. 4to. Bound uncut in a very nice recent pastiche-binding in brown half calf with elaborately gilt spine and marbled paper covered boards. With repair to title-page, not affecting text. Small restorations to upper margin of leaf A2 and A3. Brownspotted throughout. 39, (1) pp. + engraved plate.‎

‎Rare first edition of Gauss's first book in which he proved the fundamental theorem of algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. Gauss received his doctorate degree for this work, which is considered his first great work. It marks the beginning of an extraordinary ten years often referred to as his 'Triumphal Decade' with landmark achievements such as the publication of 'Disquisitiones Arithmeticae' and the calculation of the orbit of the newly discovered planet Ceres. On june 16, 1799, even before the thesis was published, Gauss was awarded the title Doctor Philosophiae after the usual requirements of an oral examination, particularly tedious to Gauss, was dropped. In a letter to Bolyai, Gauss's close friend, Gauss described his thesis: ""The title describes the main objective of the paper quite well though I devote to it only about a third of the space. The rest mainly contains history and criticisms of the works of other mathematicians (name d'Alembert, Bougainville, Euler, de Foncenex, Lagrange, and the authors of compendia - the latter will presumably not be too happy) about the subject, together with diverse remarks about the shallowness of contemporary mathematics"" ""Professor Pfaff, Gauss's formal research supervisor, shared with Gauss an interest in the foundations of geometry, but it is mere speculation that the two discussed this topic. Gauss's dissertation is about the fundamental theorem of algebra. The proof and discussion avoid the use of imaginary quantities through the work is analytic and geometric in nature"" its underlying ideas are most suitably expressed in the complex domain. Like the law of quadratic reciprocity, the fundamental theorem of algebra was a recurring topic in Gauss's mathematical work - in fact, his last mathematical paper returned to it, this time explicitly using complex numbers."" (Gauss, A Biographical Study, p. 41). ""There is only one thing wrong with this landmark in Algebra. The first two words in the title would imply that Gauss had merely added a 'new' proof to others already known. He should have omitted ""nova"". His was the first proof . Some before him had published what they supposed were proofs of this theorem - usually called the fundamental theorem of algebra - but logical and mathematical rigor Gauss insisted upon a proof, and gave the first"" (Bell, Men of Mathematics, p. 32) ""Gauss ranks, together with Archimedes and Newton, as one of the greatest geniuses in the history of mathematics."" (Printing & the Mind of Man). Dibner 114‎

Referenz des Buchhändlers : 59012

‎"GAUSS, CARL FRIEDRICH. - THE METHOD OF LEAST SQUARES IN GERMAN.‎

‎Theorie der Bewegung der Himmelskörper welche in Kegelschnitten die Sonne umlaufen. Ins Deutsche übertragen von Carl Haase. Mit einem Anhange sowie mit einer photographisches Abbildung...Gauss-Medaille...Facsimile der Gauss'schen lateinischen und deut...‎

‎Hannover, Carl Meyer, 1865. 4to. Contemp. modest hcloth. 2 orig. photographs mounted as frontispiece (Gauss-medal). 279,72,(2) pp. 3 plates, 6 tables. Internally clean.‎

‎First German edition of this milestone in mathematical statistics, first published in Latin as ""Theoria motus corporum coelestium in sectinibus conicis solem ambientum. 1809."" - In this work Gauss revealed for the first time his method of least squares. On January 1, 1801, the Italian astronomer Giuseppe Piazzi discovered the planetoid Ceres, but could only observe it for few days before it was lost in the glare of the Sun until the end of the year. After so many months of not being observed it was not possible to calculate with existing methods at which position it should reappear. However Gauss, at an age of 24, astounded when he in December predicted the exact location at which Ceres again could be observed. Gauss did not reveal how he had calculated the orbit of Ceres. First in 1809 Gauss published his second book ""Theoria motus corporum coelestium in sectionibus conicis solem ambientium"" (the offered item) in which he revealed his new method of orbit calculation. In the first part he dealt with differential equations, conic sections and elliptic orbits, while in the second part, the main part of the work, he showed how to estimate and then to refine the estimation of a planet's orbit using a new method involving minimizing the sum of squared residuals, e.g., the method of least squares. He was able to prove the correctness of the method under the assumption of normally distributed errors. It is here that the Gaussian curve, expressing statistical distribution in probablility, makes its appearance. This work, along with the 'Discuisitiones', was the fruit of the triumphal decade in Gauss' life and established his reputation as a mathematical and scientific genius of the first order. Hald: History of Mathematical Statistics 1750-1930, pp.351-357.‎

Referenz des Buchhändlers : 38464

‎"GAUSS, CARL FRIEDRICH‎

‎Theoria motus corporum coelestium in sectionibus conicis solem ambientium. - [THE METHOD OF LEAST SQUARES REVEALED]‎

‎Hamburg, Frid. Perthes & I.H. Besser, 1809. 4to (224 x 261 mm). In a later full cloth binding with gilt lettering to spine and blindtooled borders to boards. Very few occassional brownspots. A fine and clean copy. [Blank], XI, (1), 227, (1), 20, [blank] pp. + 1 folded plate.‎

‎"GAUSS, CARL FRIEDRICH.‎

‎Abhandlungen zur Methode der kleinsten Quadrate. In deutscher Sprache herausgegeben von A. Börsch und P. Simon.‎

‎Berlin, P. Stankiewicz, 1887. Cont. hcloth, rebacked with old spine preserved and with original printed wrappers pasted on covers. V,(2),290 pp. A few pencil underlinings.‎

‎"GAUSS, CARL FRIEDRICH.‎

‎Recherches Arithmétiques. Traduites par A.-C.-M. Poullet-Delisle. - [THE FIRST TRANSLATION OF GAUSS' MAIN WORK]‎

‎Paris, Courcier, 1807. 4to. (252x197mm). Nice recent half morocco over marbled boards. First and last leaves brownspotted, and even, light browning throughout. XX,(2),502 pp. (including half-title and errata). Interleaved with contemporary handwritten notes (and computations) in French.‎

‎"GAUSS, CARL FRIEDRICH. - THE CALCULUS OF VARIATIONS.‎

‎Principia generalia theoriae figurae fluidorum in statu aequilibrii.‎

‎(Göttingen, Dieterich, 1830). 4to. Partly uncut. Spine closed with paperlabel. In: ""Commentarii Societatis Regiae Scientiarum Gottingensis. Classes Mathematica"", Bd. VII. Pp. (39-) 88. Clean and fine.‎

‎"GORDAN. [PAUL ALBERT].‎

‎Die Simultanen Systeme binärer Formen. - [GORDAN ON BINARY FORMS]‎

‎Leipzig, B. G. Teubner, 1870. 8vo. Bound with the original wrappers in black full cloth with gilt lettering to spine. In ""Mathematische Annalen, 2. band, 1870"". Entire issue offered. Two library labels pasted on to pasted down front free end-paper and library stamt to verso of title page. [Gordan:] Pp. 227-280. [Entire issue: IV, 649, (1), pp.].‎

‎First printing of Gordan's important paper in which he proved that any finite system of binary forms of arbitrary degree had a complete system of invariants. These archievement earned Gordan the name ""King of invariant theory"". (Kolmogorov, Mathematics of the 19th century, p. 85).Paul Gordan, German mathematician, was a major contributor to the field of invariant theory. He collaborated with Rudolf Clebsch on both invariant theory and algebraic geometry, and also developed proofs demonstrating that the numbers e and ? are transcendent numbers, numbers that are not the root of any algebraic equation with rational coefficients. A strict mathematical logician, Gordan commented that David Hilbert's less formal approach to mathematics was ""not mathematics, it is theology."" (Schlager, Science and Its Times, P. 269)‎

Referenz des Buchhändlers : 45201

‎"GORDAN, P.,‎

‎Ueber einen Satz von Hilbert. - [COINING ""HILBERT'S THEOREM""]‎

‎Leipzig, B.G. Teubner, 1893. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. Herausgegeben von A. Clebsch und C. Neumann. 42. Band. 1. Heft."" Entire issue offered. Library-stamp to verso of title page. A fine and clean copy. [Gordan:] Pp. 132-42. [Entire issue: IV, 152 pp.].‎

‎First printing of Gordan' paper on Hilbert's (basic) theorem, in which Godan coined the term ""Hilbert's Theorem"".‎

Referenz des Buchhändlers : 44983

‎"GORDAN, P.‎

‎Ueber einen Satz von Hilbert. - [COINING ""HILBERT'S THEOREM""]‎

‎Leipzig, B.G. Teubner, 1893. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. Herausgegeben von A. Clebsch und C. Neumann. 42. Band. 1. Heft."" Entire issue offered. Library-stamp to verso of title page. A fine and clean copy. [Gordan:] Pp. 132-42. [Entire issue: IV, 152 pp.].‎

‎"GORDAN. [PAUL ALBERT].‎

‎Die Simultanen Systeme binärer Formen. - [GORDAN ON BINARY FORMS]‎

‎Leipzig, B. G. Teubner, 1870. 8vo. Bound with the original wrappers in black full cloth with gilt lettering to spine. In ""Mathematische Annalen, 2. band, 1870"". Entire issue offered. Two library labels pasted on to pasted down front free end-paper and library stamt to verso of title page. [Gordan:] Pp. 227-280. [Entire issue: IV, 649, (1), pp.].‎

‎"GREEN, GEORG.‎

‎Ein Versuch die Mathematische Analysis auf die Theorieen der Elektricität und Magnetismus anzuwenden. (Veröffentlich 1828 in Nottingham.). Hrs. von A.J. von Oettingen und A. Wangerin.‎

‎Leipz, Wilhelm Engelmann, 1895. Orig. printed boards. Spine ends worn. 140 pp. (Ostwald's Klassiker der exacten Wissenschaften. Nr.61).‎

‎First German edition of Greens importent work on themathematication of electricity and magnetism from 1828, in which he published the ""Green Theorem"", -""Although published very obscurely, this book became recognized as a major text in potential theory after gaining publicity from the 1850s. The integral theorem and function which came to carry Green's name gained special attention.""(Grattan-Guiness).‎

Referenz des Buchhändlers : 39705

‎"GRAFFENRIED, JOHAN RUDOLFF von.‎

‎Arithmeticae Logisticae. Popularis Libri IIII. In welscher der Algorithmus in ganzen Zahlen und Fracturen/ sampt der Proportionen... Allen freyen Mathematischen Kunstbegierigen/ und jedermenniglich zu gutem auss den fürnembsten Authoren zusammen getra...‎

‎Bern, Abraham Weerli, (1618) - 1619. 4to. Contemporary full calf binding with brass clasps. Five raised bands and single gilt line-ornamentation to back. Single gilt line-borders to boards. Professional, very neat restorations to back. Some browning and a, mostly marginal, damp-stain to first leaves, but overall a very nice and attractive copy. Many diagrams and computations in the text. Title-page in red and black, with woodcut ornamental border. Woodcut title-pages to second, third, and fourth parts (all part of the collation, all dated 1618). 1/3 page woodcut at end. (56), 704, (16) pp. + two folded diagrams.‎

‎"GROTHENDIECK, A.‎

‎On the de Rham Cohomology of Algebraic Varieties. - [THE FOUNDATION OF CRYSTALLINE COHOMOLOGY]‎

‎[Paris, Presses Universitaires de France, 1966]. 4to. In the original stapled blank blue printed wrappers. Offprint from ""Institut des Hautes Études Scientifiques. Publications Mathématiques"" No. 29. Light wear to extrimities, otherwise fine and clean. Pp. 95-103, (1).‎

‎"GUDERMANN, CHR.‎

‎De curva quarti ordinis sphaerica, de Circulari scalena.‎

‎Berlin, G. Reimer, 1852. 4to. In the original printed wrappers, without back strip. In ""Journal für die reine und angewandte Mathematik"", 43. band, Heft 2, 1852. Entire second heft offered. Fine and clean. Pp. 93-113. [Entire volume: Pp. 93-184 + 3 plates.].‎

‎First printing.‎

Referenz des Buchhändlers : 47534

‎"GUDERMANN, CHRISTOPH.‎

‎Potential oder zyklisch-hyperbolische Funktionen I - II.‎

‎(Berlin, G. Reimer, 1832) 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 8. Band, 1832"", without backstrip. Fine and clean. pp. 64-116"" Pp. 194-212.‎

‎First printing of Gudermann extensive and important papers on hyperbolic functions. During 1830ies Gudermann focused his work on these functions and published extensive on the subject. It was later coined the Gudermannian function.The function was introduced by Johann Heinrich Lambert in the 1760s at the same time as the hyperbolic functions. He called it the ""transcendent angle,"" and it went by various names until 1862 when Cayley suggested it be given its current name as a tribute to Gudermann's work in the 1830ies on the theory of special functions. The present paper together with two later published papers were collected in Theorie der potenzial- oder cyklisch-hyperbolischen functionen (1833), a book which expounded sinh and cosh to a wide audience.The issue also contain a paper by the famous Norwegian mathematician Niels Henrik Abel.""Gudermann devoted much more attention to the theory of special functions. After the earlier works of Leonhard Euler, John Landen, and A. M. Legendre (Gauss's results were still in manuscript), Niels Abel's studies on elliptical functions, published mostly in A. L. Crelle's Journal für reine und angewandte Mathematik, represented an important divide in treating this area. In 1829 Carl Jacobi's book Fundamenta nova theoriae functionum ellipticarum was published. At the time Gudermann was one of the first mathematicians to expand on these results. Beginning with volume 6 (1830) of Crelle's Journal, he published a series of papers which he later summarized in two books: Theorie der Potenzialoder cyklisch-hyperbolischen Functionen (1833) and Theorie der Modular-Functionen und der Modular-Integrale (1844), which were to have had a sequel which was never written."" (DSB). Gudermann is known today for being the teacher of Karl Weierstrass, who took Gudermann's course in elliptic functions in 1839, the first to be taught in any institute. Weierstrass was greatly influenced by this course, which marked the direction of his own research.‎

Referenz des Buchhändlers : 49082

‎"GUDERMANN, CHRISTOPH.‎

‎Theorie der Modular-Functionen und der Modular-Integrale, Allgemeiner Charakter der Potenzial-Functionen (+) Theorie der Modular-Functionen und der Modular-Integrale.‎

‎Berlin, G. Reimer, 1838. 4to. In ""Journal für die reine und angewandte Mathematik, 18. Band, 1-2 Heft, 1838"". Both issues in the original printed wrappers, without backstrip. Fine and clean. [Gudermann, 1 heft:] Pp. 1-54. [Gudermann, 2 heft:] Pp. 142-175. [Entire issue, heft 1: IV, 100, (2) pp. 2 Heft: 101-188, (2) pp. + 2 plates, one of them detached.].‎

‎First printing of Gudermann's two papers on modular functions and modular integrals, ideas which anticipated his 1844-book.""Gudermann devoted much more attention to the theory of special functions. After the earlier works of Leonhard Euler, John Landen, and A. M. Legendre (Gauss's results were still in manuscript), Niels Abel's studies on elliptical functions, published mostly in A. L. Crelle's Journal für reine und angewandte Mathematik, represented an important divide in treating this area. In 1829 Carl Jacobi's book Fundamenta nova theoriae functionum ellipticarum was published. At the time Gudermann was one of the first mathematicians to expand on these results. Beginning with volume 6 (1830) of Crelle's Journal, he published a series of papers which he later summarized in two books: Theorie der Potenzialoder cyklisch-hyperbolischen Functionen (1833) and Theorie der Modular-Functionen und der Modular-Integrale (1844), which were to have had a sequel which was never written."" (DSB).‎

Referenz des Buchhändlers : 45138

‎"GUDERMANN, CHRISTOPH.‎

‎Theorie der Potenzial- oder der cyklisch- hyperbolischen Functionen. (Fortsetzung der Abhandlung No. 1. im vorigen Hefte). - [GUDERMANNIAN FUNCTION]‎

‎Berlin, G. Reimer, 1830. 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 6. Band, 1830""., without backstrip. Fine and clean. [Gudermann:] Pp. 162-194. [Entire volue: Pp. 147-214].‎

‎First printing of Gudermann extensive and important second paper on hyperbolic functions. During 1830ies Gudermann focused his work on these functions and published extensive on the subject, the present paper being the first. It was later coined the Gudermannian function.The function was introduced by Johann Heinrich Lambert in the 1760s at the same time as the hyperbolic functions. He called it the ""transcendent angle,"" and it went by various names until 1862 when Cayley suggested it be given its current name as a tribute to Gudermann's work in the 1830ies on the theory of special functions. The present paper together with two later published papers were collected in Theorie der potenzial- oder cyklisch-hyperbolischen functionen (1833), a book which expounded sinh and cosh to a wide audience.The issue also contain a paper by the famous Norwegian mathematician Niels Henrik Abel.""Gudermann devoted much more attention to the theory of special functions. After the earlier works of Leonhard Euler, John Landen, and A. M. Legendre (Gauss's results were still in manuscript), Niels Abel's studies on elliptical functions, published mostly in A. L. Crelle's Journal für reine und angewandte Mathematik, represented an important divide in treating this area. In 1829 Carl Jacobi's book Fundamenta nova theoriae functionum ellipticarum was published. At the time Gudermann was one of the first mathematicians to expand on these results. Beginning with volume 6 (1830) of Crelle's Journal, he published a series of papers which he later summarized in two books: Theorie der Potenzialoder cyklisch-hyperbolischen Functionen (1833) and Theorie der Modular-Functionen und der Modular-Integrale (1844), which were to have had a sequel which was never written."" (DSB).Gudermann is known today for being the teacher of Karl Weierstrass, who took Gudermann's course in elliptic functions in 1839, the first to be taught in any institute. Weierstrass was greatly influenced by this course, which marked the direction of his own research.‎

Referenz des Buchhändlers : 47281

‎"GUDERMANN, CHRISTOPH.‎

‎Beweis des im zweiten Bande dieses Journals Seite 190. von Herrn Steiner aufgestellten Lehrsatzes No. 27. und Ableitung anderer ebenso einfacher Relationen.‎

‎(Berlin, G. Reimer, 1832) 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 8. Band, 1832"", without backstrip. Fine and clean. pp. 160-68.‎

‎"GUDERMANN, CHRISTOPH.‎

‎Theorie der Modular-Functionen und der Modular-Integrale, Allgemeiner Charakter der Potenzial-Functionen (+) Theorie der Modular-Functionen und der Modular-Integrale.‎

‎Berlin, G. Reimer, 1838. 4to. In ""Journal für die reine und angewandte Mathematik, 18. Band, 1-2 Heft, 1838"". Both issues in the original printed wrappers, without backstrip. Fine and clean. [Gudermann, 1 heft:] Pp. 1-54. [Gudermann, 2 heft:] Pp. 142-175. [Entire issue, heft 1: IV, 100, (2) pp. 2 Heft: 101-188, (2) pp. + 2 plates, one of them detached.].‎

‎"GUDERMANN, CHRISTOPH.‎

‎Theorie der Potenzial- oder der cyklisch- hyperbolischen Functionen. - [GUDERMANNIAN FUNCTION]‎

‎Berlin, G. Reimer, 1830. 4to. In ""Journal für die reine und angewandte Mathematik, 6. Band, 1 Heft, 1830"". In the original printed wrappers, without backstrip. Fine and clean. [Gudermann:] Pp. 1-39. [Entire issue: Pp. 106 pp. + 1 folded plate. ].‎

‎"GULDBERG, ALF.‎

‎Om integration af Differentialligninger af 2den orden.‎

‎Christiania, Jacob Dybwad, 1895. Uncut in orig. printed wrappers. Offprint from ""Christiania Videnskabs-Selskabs Forhandlinger 1895. No. 6"". 48 pp.‎

‎"GYLDÉN, HUGO.‎

‎Untersuchungen über die Convergenz der Reihen, welche zur Darstellung der Coordinaten der Planaten angewendet.‎

‎Berlin, Stockholm, Paris, Beijer, 1887. 4to. With the original wrappers in ""Acta Mathematica, 9:3. Band]. No backstrip. Fine and clean. Pp. 185-294. [Entire issue: Pp. 185-320]‎

‎First printing of Gyldén's paper on planetary coordinates. Hugo Gyldén was the most impotant swedish astronomer during the 19th century and he initiated celestial mechanics in Sweden.‎

Referenz des Buchhändlers : 45903